Meeting again at the start on a circular track: On a 5 km circular track, A, B, and C start together in the same direction at 2.5 km/h, 3 km/h, and 2 km/h, respectively. After how many hours will all three meet again at the starting point?
Aptitude
Races and Games
Difficulty: Medium
Choose an option
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A30 hours
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B6 hours
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C10 hours
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D15 hours
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ENone of these
Answer
Correct Answer: 10 hours
Explanation
Introduction / Context:When multiple runners set off on a circular track, they are all back at the start together at the least common multiple (LCM) of their individual lap times.
Given Data / Assumptions:
- Track length = 5 km.
- Speeds: 2.5, 3, and 2 km/h; constant speeds.
Concept / Approach:Compute lap periods: T1 = 5/2.5 = 2 h; T2 = 5/3 = 5/3 h; T3 = 5/2 = 2.5 h. The required time is LCM(T1, T2, T3).
Step-by-Step Solution:
T1 = 2 h; T2 = 5/3 h; T3 = 5/2 hLCM(2, 5/3, 5/2) = 10 h (smallest t with t/Ti all integers)Check: 10/2 = 5; 10/(5/3) = 6; 10/(5/2) = 4 — all integersVerification / Alternative check:LCM via integerizing denominators also yields 10 h.
Why Other Options Are Wrong:6/15/30 are common distractors but fail integrality for at least one runner.
Common Pitfalls:Using arithmetic mean or max instead of LCM of lap periods.
Final Answer:10 hours